Ibn-al-Haitam, al-Hasan Ibn-al-Hasan; Witelo; Risner, Friedrich, Opticae thesavrvs Alhazeni Arabis libri septem, nunc primùm editi. Eivsdem liber De Crepvscvlis & Nubium ascensionibus. Item Vitellonis Thuvringopoloni Libri X. Omnes instaurati, figuris illustrati & aucti, adiectis etiam in Alhazenum commentarijs, a Federico Risnero, 1572

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        <div xml:id="echoid-div290" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s7686" xml:space="preserve">
              <pb o="131" file="0137" n="137" rhead="OPTICAE LIBER V"/>
            ret continua cum apparente oculo:</s>
            <s xml:id="echoid-s7687" xml:space="preserve"> & ſemper in totali forma apparente eundem tenet locum & ſi-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s7688" xml:space="preserve"> Cuiuſcunq;</s>
            <s xml:id="echoid-s7689" xml:space="preserve"> uerò puncti imago, præter centrũ uiſus, ad ſpeculum accedit, mouetur declinatè:</s>
            <s xml:id="echoid-s7690" xml:space="preserve">
              <lb/>
            quare nõ durat ei ſimilitudo ſitus, reſpectu uiſus:</s>
            <s xml:id="echoid-s7691" xml:space="preserve"> & perpendicularis à puncto uiſo ad ſpeculũ ducta,
              <lb/>
            cadit ſuper centrũ ſphęrę:</s>
            <s xml:id="echoid-s7692" xml:space="preserve"> in qua quidẽ perpẽdiculari obſeruat imago ſimilitu dinẽ ſitus.</s>
            <s xml:id="echoid-s7693" xml:space="preserve"> Nõ eſt ergo
              <lb/>
            punctum, in quo cõprehenſa imago ſeruet ſimilitudinẽ ſitus, niſi in perpendiculari illa.</s>
            <s xml:id="echoid-s7694" xml:space="preserve"> Et cũ opor-
              <lb/>
            teat ipſam comprehendi in linea reflexionis, [per 21 n 4] comprehendetur in concurſu huius lineæ
              <lb/>
            cum hac perpendiculari.</s>
            <s xml:id="echoid-s7695" xml:space="preserve"> Iam ergo aſsignauimus cauſſam huius rei.</s>
            <s xml:id="echoid-s7696" xml:space="preserve"> Verùm rerum naturaliũ ſtatus
              <lb/>
            reſpicit ſitus ſuorum principiorũ, & principia rerum naturaliũ ſunt occulta.</s>
            <s xml:id="echoid-s7697" xml:space="preserve"> Idem erit modus proba
              <lb/>
            tionis in ſpeculo ſphærico concauo.</s>
            <s xml:id="echoid-s7698" xml:space="preserve"> Similiter in pyramidali concauo, uel extrà polito.</s>
            <s xml:id="echoid-s7699" xml:space="preserve"> Et uniuerſali
              <lb/>
            ter erit locus imaginis in perpendiculari in quocunq;</s>
            <s xml:id="echoid-s7700" xml:space="preserve"> ſpeculo:</s>
            <s xml:id="echoid-s7701" xml:space="preserve"> quoniam non eſt locus extra perpen
              <lb/>
            pendicularem, in quo forma obſeruet ſimilitudinem ſitus & identitatem.</s>
            <s xml:id="echoid-s7702" xml:space="preserve"> His explanatis reſtat de-
              <lb/>
            monſtratiuè declarare locum imaginis, in qualibet ſpeculorum ſpecie.</s>
            <s xml:id="echoid-s7703" xml:space="preserve"> Dicimus ergo, quod linea,
              <lb/>
            per quam reflectitur forma puncti cuiuslibet comprehenſi à uiſu in ſpeculo plano, quando ipſum e-
              <lb/>
            greſſum eſt à perpendiculari, quæ à centro uiſus cadit in ſuperficiem ſpeculi plani:</s>
            <s xml:id="echoid-s7704" xml:space="preserve"> concurret cum
              <lb/>
            perpendiculari, producta ab illo puncto ad ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s7705" xml:space="preserve"> & erit punctum concurſus (qui eſt
              <lb/>
            locus imaginis) ultra ſpeculum:</s>
            <s xml:id="echoid-s7706" xml:space="preserve"> & erit longitudo illius à ſuperficie ſpeculi, æqualis longitudini pun
              <lb/>
            cti uiſi à ſuperficie ſpeculi:</s>
            <s xml:id="echoid-s7707" xml:space="preserve"> & uiſus non acquirit imaginem puncti uiſi, niſi in loco illo.</s>
            <s xml:id="echoid-s7708" xml:space="preserve"> Et quodcunq;</s>
            <s xml:id="echoid-s7709" xml:space="preserve">
              <lb/>
            punctum acquirit uiſus in hoc ſpeculo:</s>
            <s xml:id="echoid-s7710" xml:space="preserve"> non apparebit ex eo, niſi unica imago.</s>
            <s xml:id="echoid-s7711" xml:space="preserve"> Quodcunq;</s>
            <s xml:id="echoid-s7712" xml:space="preserve"> autẽ pun
              <lb/>
            ctum comprehendit uiſus in ſpeculo ſphærico extrà polito, quando egreditur forma à perpendicu-
              <lb/>
            lari, ducta à centro uiſus ad centrum ſpeculi:</s>
            <s xml:id="echoid-s7713" xml:space="preserve"> linea, per quã reflectitur imago ad oculum, concurret
              <lb/>
            cum linea producta à puncto illo ad centrum ſpeculi:</s>
            <s xml:id="echoid-s7714" xml:space="preserve"> quæ linea eſt perpendicularis, ducta à puncto
              <lb/>
            illo orthogonaliter ſuper lineã, contingentẽ lineam cõmunem ſuperficiei reflexionis, & ſuperficiei
              <lb/>
            ſpeculi.</s>
            <s xml:id="echoid-s7715" xml:space="preserve"> Et ſitus puncti concurſus, qui eſt locus imaginis, à ſuperficie ſpeculi erit ſecundũ ſitum ui-
              <lb/>
            ſus à ſuperficie ſpeculi.</s>
            <s xml:id="echoid-s7716" xml:space="preserve"> Et forſitan erit punctum concurſus ultra ſpeculum, forſitan in ſuperficie ſpe
              <lb/>
            culi, forſitan intra ſpeculum.</s>
            <s xml:id="echoid-s7717" xml:space="preserve"> Et uiſus comprehendit imagines omnes ultra ſpeculum, licet diuerſa
              <lb/>
            ſint earum loca:</s>
            <s xml:id="echoid-s7718" xml:space="preserve"> & non comprehendit locum cuiuslibet imaginis, niſi ſyllogiſticè in ſuperficie ſpe-
              <lb/>
            culi.</s>
            <s xml:id="echoid-s7719" xml:space="preserve"> Et quodlibet punctum comprehenſum in hoc ſpeculo, non prætendit, niſi unam imaginem.</s>
            <s xml:id="echoid-s7720" xml:space="preserve"> In
              <lb/>
            ſpeculo columnari extrà polito, & pyramidali extrà polito, quodcunq;</s>
            <s xml:id="echoid-s7721" xml:space="preserve"> punctum comprehendit ui-
              <lb/>
            ſus, cum fuerit extra perpendicularem, ductam à centro uiſus, orthogonalem ſuper ſuperficiem con
              <lb/>
            tingentem ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s7722" xml:space="preserve"> linea, per quam reflectitur forma ad uiſum, concurret cum perpendi
              <lb/>
            culari, ducta ab illo puncto ſuper rectam lineam, contingentem lineam communem ſuperficiei re-
              <lb/>
            flexionis, & ſpeculi.</s>
            <s xml:id="echoid-s7723" xml:space="preserve"> Et loca imagihum horum ſpeculorum quædam ſunt ultra ſuperficiem ſpeculi:</s>
            <s xml:id="echoid-s7724" xml:space="preserve">
              <lb/>
            quædam in ſuperficie:</s>
            <s xml:id="echoid-s7725" xml:space="preserve"> quædam citra.</s>
            <s xml:id="echoid-s7726" xml:space="preserve"> Et uiſus acquirit omnes imagines horum ſpeculorum ultra ſu
              <lb/>
            perficiem ſpeculi.</s>
            <s xml:id="echoid-s7727" xml:space="preserve"> Et quodcunq;</s>
            <s xml:id="echoid-s7728" xml:space="preserve"> punctum comprehendit uiſus in his ſpeculis, non efficit, niſi unam
              <lb/>
            imaginem tantùm.</s>
            <s xml:id="echoid-s7729" xml:space="preserve"> In ſpeculo ſphærico concauo lineæ, per quas reflectuntur formæ punctorũ uiſo-
              <lb/>
            rum:</s>
            <s xml:id="echoid-s7730" xml:space="preserve"> quædam concurrunt cum perpendicularibus, ductis à punctis illis ſuper lineas, contingentes
              <lb/>
            lineas communes ſuperficiei ſpeculi & ſuperficiei reflexionis:</s>
            <s xml:id="echoid-s7731" xml:space="preserve"> quædam ſunt æquidiſtantes his per-
              <lb/>
            pendicularibus.</s>
            <s xml:id="echoid-s7732" xml:space="preserve"> Et earum, quæ concurrunt cum perpendicularibus, quædam habent locum con-
              <lb/>
            curſus (qui eſt locus imaginis) ultra ſpeculum:</s>
            <s xml:id="echoid-s7733" xml:space="preserve"> quædam citra ſpeculum.</s>
            <s xml:id="echoid-s7734" xml:space="preserve"> Et quæ citra ſpeculum ha-
              <lb/>
            bent:</s>
            <s xml:id="echoid-s7735" xml:space="preserve"> quædam inter uiſum & ſpeculum:</s>
            <s xml:id="echoid-s7736" xml:space="preserve"> quædam ſuper ipſum centrũ uiſus:</s>
            <s xml:id="echoid-s7737" xml:space="preserve"> quædam ultra centrum
              <lb/>
            uiſus.</s>
            <s xml:id="echoid-s7738" xml:space="preserve"> Et uiſus quaſdam formarum rerum uiſarum, quas acquirit in his ſpeculis, comprehendit in lo
              <lb/>
            co imaginis, qui eſt punctum concurſus:</s>
            <s xml:id="echoid-s7739" xml:space="preserve"> & hæ ſunt, quas uiſus certò comprehendit:</s>
            <s xml:id="echoid-s7740" xml:space="preserve"> quaſdam com-
              <lb/>
            prehendit extra locum concurſus:</s>
            <s xml:id="echoid-s7741" xml:space="preserve"> & eſt comprehenſio ſine certitudine.</s>
            <s xml:id="echoid-s7742" xml:space="preserve"> Et res uiſæ, quas acquirit ui
              <lb/>
            ſus in hoc ſpeculo, quædam unam præ ſe ferunt imaginem tantùm:</s>
            <s xml:id="echoid-s7743" xml:space="preserve"> quædam duas:</s>
            <s xml:id="echoid-s7744" xml:space="preserve"> quædam tres:</s>
            <s xml:id="echoid-s7745" xml:space="preserve">
              <lb/>
            quædã quatuor.</s>
            <s xml:id="echoid-s7746" xml:space="preserve"> Nec poteſt eſſe, quod una res prætendat plures.</s>
            <s xml:id="echoid-s7747" xml:space="preserve"> In ſpeculo pyramidali cõcauo & co
              <lb/>
            lumnari concauo lineæ, per quas reflectuntur formæ ad uiſum:</s>
            <s xml:id="echoid-s7748" xml:space="preserve"> quædam concurrunt cum perpendi
              <lb/>
            cularibus, ductis à punctis uiſis ſuper lineas, contingentes lineas communes:</s>
            <s xml:id="echoid-s7749" xml:space="preserve"> & quædam ſunt æqui
              <lb/>
            diſtantes perpendιcularibus.</s>
            <s xml:id="echoid-s7750" xml:space="preserve"> Quæ concurrunt cum perpendicularibus:</s>
            <s xml:id="echoid-s7751" xml:space="preserve"> quædam habent concur-
              <lb/>
            ſum ultra ſpeculum:</s>
            <s xml:id="echoid-s7752" xml:space="preserve"> quædam citra.</s>
            <s xml:id="echoid-s7753" xml:space="preserve"> Quæ autem citra:</s>
            <s xml:id="echoid-s7754" xml:space="preserve"> quædam inter ſpeculum & uiſum:</s>
            <s xml:id="echoid-s7755" xml:space="preserve"> quædam ſu
              <lb/>
            per centrum uiſus:</s>
            <s xml:id="echoid-s7756" xml:space="preserve"> quædam ultra centrum uiſus.</s>
            <s xml:id="echoid-s7757" xml:space="preserve"> Et comprehenſio rerum uiſarum in hoc ſpeculo
              <lb/>
            per uiſum, quædam fit in loco imaginis (qui eſt locus concurſus) quædam extra locum concurſus.</s>
            <s xml:id="echoid-s7758" xml:space="preserve">
              <lb/>
            Et eorum, quæ comprehenduntur, aliud prætendit unam imaginem tantùm:</s>
            <s xml:id="echoid-s7759" xml:space="preserve"> aliud duas:</s>
            <s xml:id="echoid-s7760" xml:space="preserve"> aliud tres:</s>
            <s xml:id="echoid-s7761" xml:space="preserve">
              <lb/>
            alind quatuor.</s>
            <s xml:id="echoid-s7762" xml:space="preserve"> Nec aliquod eſt, quod poſsit prætendere plures, quàm quatuor.</s>
            <s xml:id="echoid-s7763" xml:space="preserve"> Et nos declarabi-
              <lb/>
            mus hæc omnia demonſtratiuè.</s>
            <s xml:id="echoid-s7764" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div291" type="section" level="0" n="0">
          <head xml:id="echoid-head314" xml:space="preserve" style="it">11. Viſibile & imago à ſpeculi plani ſuperficie in oppoſit {as} partes æquabiliter distant. 49 p 5.</head>
          <p>
            <s xml:id="echoid-s7765" xml:space="preserve">SIt a punctum uiſum:</s>
            <s xml:id="echoid-s7766" xml:space="preserve"> b centrum uiſus:</s>
            <s xml:id="echoid-s7767" xml:space="preserve"> c d e ſpeculum planum:</s>
            <s xml:id="echoid-s7768" xml:space="preserve"> & ſit d punctum reflexionis:</s>
            <s xml:id="echoid-s7769" xml:space="preserve"> c d e
              <lb/>
            linea communis ſuperficiei reflexionis & ſuperficiei ſpeculi.</s>
            <s xml:id="echoid-s7770" xml:space="preserve"> A puncto d ducatur d f perpendi-
              <lb/>
            cularis ſuper lineã cõmunẽ:</s>
            <s xml:id="echoid-s7771" xml:space="preserve"> [per 11 p 1] & à puncto a ducatur perpendicularis ſuper ſpeculi ſu
              <lb/>
            perficiẽ, [per 11 p 11] quæ ſit a c, & producatur ultra ſpeculũ:</s>
            <s xml:id="echoid-s7772" xml:space="preserve"> & a d ſit linea, per quã forma accedit ad
              <lb/>
            ſpeculũ:</s>
            <s xml:id="echoid-s7773" xml:space="preserve"> b d, per quã reflectitur ad uiſum.</s>
            <s xml:id="echoid-s7774" xml:space="preserve"> Igitur b d, f d, a d, ſunt in ſuperficie reflexionis [per 23 n 4.</s>
            <s xml:id="echoid-s7775" xml:space="preserve">]
              <lb/>
            Et cũ f d ſit æquidiſtãs a c [per 28 p 1:</s>
            <s xml:id="echoid-s7776" xml:space="preserve"> quia cũ a c ſit քpẽdicularis ſuperficiei ſpeculi per fabricatiõem:</s>
            <s xml:id="echoid-s7777" xml:space="preserve">
              <lb/>
            erit perpẽdicularis lineę c d e per 3 d 11] & [per 13 p 11] d b declinata ſit ſuper f d, cõcurret [per lemma
              <lb/>
            Procli ad 29 p 1] b d cũ a c.</s>
            <s xml:id="echoid-s7778" xml:space="preserve"> Cõcurrat ergo in puncto g.</s>
            <s xml:id="echoid-s7779" xml:space="preserve"> Dico, quòd g c eſt æqualis c a.</s>
            <s xml:id="echoid-s7780" xml:space="preserve"> Quoniã enim
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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